[Ifeffit] What confidence limit is implied in the error bars for least-squares fitting in Athena

[Wayne Lukens]

Hi Andrew,

If your issue is whether or not a phase with a amplitude of
0.049(3) is actually present in your sample, then you want to
use an F-test.  The probability of of the F-distribution is
the probability that the improvement in the fit (due in this
case to adding a component with an amplitude of 0.049) could
be due to random error.  The general rule of thumb is that if
the probability is less than 0.05, than improvement in the
fit is significant, and the component can be considered to be
observed.

Unlike the standard deviations of the fitting parameters, the F-test
does not depend on having an accurate description of the uncertainty
of the data.

Sincerely,

Wayne

Matt Newville wrote:
>> Athena uses Ifeffit's minimize function.  As you say, the data
>> uncertainty is set to one, so the diagonals of the covarience matrix
>> will be orders of magnitude too small.  My understanding is that
>> Ifeffit rescales the error bars on the variable parameters in the same
>> manner as the feffit function does -- that is, by the square root of
>> reduced chi-square.
>>
>> In that case, the error bars are reported are 1-sigma error bars given
>> the assumption that the fit is, in fact, a good fit.
>>
>> Or do I not understand what minimize is doing?  Or are there too many
>> possible meanings of the word "sigma" in this context such that we are
>> talking about different things?
>>
> 
> Yes, that is all correct  (and the reference manual is no doubt
> confusing!!)  It asserts the fit is good (and that all the data points
> are independent), and so asserts the uncertainty in the data is the
> typical misfit of data-model.  And with that estimate, it reports
> 1-sigma uncertainties in the parameters.
> 
> But that's not using an actual estimate of sigma from the data (unless
> explicitly provided).  So the value of chi-square is not scaled
> correctly.
> 
> --Matt
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